General Relativity.

Dr. Milo Wolff writes:The Wave Structure of fundamental Particles evolved over five years. It began with a simple speculation that waves in Space could explain the de Broglie wavelength. It continued to agree with more laws and observations than I first expected and I was amazed. The 'Particle' is two identical spherical waves travelling radially in opposite directions so that together they form a spherical standing wave.The wave which travels inward towards the center is called an In-Wave, and the wave travelling outward is an Out-Wave. The nominal location of the 'Partical' is the Wave-Center, but as must be true for any charged Particle, it has presence everywhere in Space because the charged forces extend throughout the Universe.
How do Solid Bodies form from Waves?-The solid crystal array is a matrix of atoms held rigidly in space. How are the atoms suspended in space? We must conclude that the crystal's rigidity derives from fixed standing waves propagating in a rigid wave medium.Calculations for diamonds and nuclear structure yields an enormous rigidity. This is really a separate argument about the rigidity of space, which is one of its properties.
What is a Light 'Photon'? -Two Spherical Standing Waves
(SSW) oscillators exchange energy much like classical coupled oscillators, such as electric circuits or joined pendulums. The coupling provided by the non-linear centers of the resonances (high Wave-Density Wave - Centers) allows them to shift frequency patterned by the modulation of each other's In and Out-Waves. Since significant coupling can only occure between two oscillators which possess the same resonant elements, the frequency (energy) take place between two resonances, energy seems to be transported from the center of one resonance to another. We observe a loss of energy where frequency decreases and added energy where it increases. The exchange appears to travel with the speed of the In-Waves of the receiving resonance which is c, the velocity of light. When large numbers of changes occure together, we can sample part of it and see a beam of light (which causes the continuous electromagnetic waves of Modern Physics). When single exchanges occure we see 'photons' as discrete Standing Wave interactions. Thus the transitory modulated waves travelling between two resonances create the illusion of the 'photon particle'.

the amplitude does correspond to the energy, or the volume of a sound

The amplitude is a bit more difficult, but it basically measures the energy of the wave.

madeofstarstuff writes:Why this is so, and what frequency and energy have to do with one another outside of just saying that E=hf, is what Ben is asking about, I assume.

Photon energy is inversely proportional to photon wave length; the shorter the wavelength, the greater the energy. Since photon speed through space is a constant, shorter wavelengths must pass a point in space in less time than longer wave lengths. Because of this, and the fact that the maximum possible electric and magnetic amplitude of any point in space is a certain finite value, photon action, expressed as Joule-seconds is a constant for all photons regardless of frequency. Planck's constant is this amount of electromagnetic amplitude available at any one point in space. Note that it is not a property of a photon, but rather a property of space itself. It is therefore not only the maximum amount but also the minimum amount of action available for a photon in space.